NUMBERS IN STANDARD FORM WORKSHEET

Problems 1-7 : Write the given number in standard form.

Problem 1 :

50000

Problem 2 :

4800

Problem 3 :

61700000

Problem 4 :

0.00000006

Problem 5 :

0.000574

Problem 6 :

37341000000

Problem 7 :

0.000000000000412

Problems 8-18 : Calculate, write your answer in standard form.

Problem 8 :

(2.05 x 10⁵) x (8.17 x 10³)

Problem 9 :

(4 x 10⁵) x (2 x 10⁴)

Problem 10 :

(5 x 10⁶) x (7 x 10⁸)

Problem 11 :

(3 x 10⁴) ÷ (6 x 10^-3)

Problem 12 :

(2.1 x 10^-5) ÷ (7 x 10^-4)

Problem 13 :

(5 x 10⁴)²

Problem 14 :

(2.5 x 10³) + (9.8 x 10³)

Problem 15 :

(2.78 x 10²) + (5.63 x 10⁵)

Problem 16 :

(7.58 x 10²) + (6.45. x 10^-1)

Problem 17 :

(5.64 x 10³) - (3.98. x 10³)

Problem 18 :

(3.99 x 10²) - (4.7. x 10^-2)

Problem 19 :

Write three hundred thousand in standard form.

Problem 20 :

Write five million in standard form.

Problem 21 :

Work out five million multiplied by three hundred thousand. Give your answer in standard form.

Problem 22 :

How many grams are there in 2500 kilograms? Give your answer in standard form.

Answers

1. Answer :

In 50000, there is no decimal point. So, assume there is a decimal point at the end.

50000.

Add the decimal point after the first nonzero digit.

5.0000

Count the number of digits that the decimal point is shifted. The decimal point is shifted four digits to the left. Take 4 as exponent for 10 and 10⁴ can be used to write the given number in standard form.

50000 = 5.0 x 10⁴

2. Answer :

In 4800, there is no decimal point. So, assume there is a decimal point at the end.

4800.

Add the decimal point after the first nonzero digit.

4.800

The decimal point is shifted three digits to the left. Take 3 as exponent for 10 and 10³ can be used to write the given number in standard form.

4800 = 4.8x 10³

3. Answer :

In 61700000, there is no decimal point. So, assume there is a decimal point at the end.

61700000.

Add the decimal point after the first nonzero digit.

6.1700000

The decimal point is shifted seven digits to the left. Take 7 as exponent for 10 and 10⁷ can be used to write the given number in standard form.

61700000 = 6.17x 10⁷

4. Answer :

0.00000008

Add the decimal point after the first nonzero digit.

8.0

The decimal point is shifted eight digits to the right. Take -8 as exponent for 10 and 10^-8 can be used to write the given number in standard form.

0.00000008 = 8.0 x 10^-8

5. Answer :

0.000574

Add the decimal point after the first nonzero digit.

5.74

The decimal point is shifted four digits to the right. Take -4 as exponent for 10 and 10^-4 can be used to write the given number in standard form.

0.000574 = 5.74 x 10^-4

6. Answer :

In 37341000000, there is no decimal point. So, assume there is a decimal point at the end.

37341000000.

Add the decimal point after the first nonzero digit.

3.7341000000

The decimal point is shifted ten digits to the left. Take 10 as exponent for 10 and 10¹⁰ can be used to write the given number in standard form.

37341000000 = 3.7341 x 10¹⁰

7. Answer :

0.000000000000412

Add the decimal point after the first nonzero digit.

4.12

The decimal point is shifted thirteen digits to the right. Take -13 as exponent for 10 and 10^-13 can be used to write the given number in standard form.

0.000000000000412 = 4.12 x 10^-13

8. Answer :

= (2.05 x 10⁵) x (8.17 x 10³)

= (2.05 x 8.17) x (10⁵ x 10³)

= 16.7485 x 10^{5 + 3}

= 16.7485 x 10⁸

= 1.67485 x 10¹ x 10⁸

= 1.67485 x 10^{1 + 8}

= 1.67485 x 10⁹

9. Answer :

= (4 x 10⁵) x (2 x 10⁴)

= (4 x 2) x (10⁵ x 10⁴)

= 8 x 10^{5 + 4}

= 8.0 x 10⁹

10. Answer :

= (5 x 10⁶) x (7 x 10⁸)

= (5 x 7) x (10⁶ x 10⁸)

= 35 x 10^{6 + 8}

= 35 x 10¹⁴

= 3.5 x 10¹ x 10¹⁴

= 3.5 x 10^{1 + 14}

= 3.5 x 10¹⁵

11. Answer :

= (3 ÷ 6) x (10⁴ ÷ 10^-3)

= 0.5 x 10^{4 - (-3)}

= 0.5 x 10^{4 + 3}

= 0.5 x 10⁷

= 5.0 x 10¹ x 10⁷

= 5.0 x 10^{1 + 7}

= 5.0 x 10⁸

12. Answer :

= (2.1 x 10^-5) ÷ (7 x 10^-4)

= (2.1 ÷ 7) x (10^-5 ÷ 10^-4)

= 0.3 x 10^{-5 - (-4)}

= 0.3 x 10^{-5 + 4}

= 0.3 x 10^-1

= 3.0 x 10¹ x 10^-1

= 3.0 x 10^{1 + (-1)}

= 3.0 x 10^{1 - 1}

= 3.0 x 10⁰

13. Answer :

= (5 x 10⁴)²

= (5 x 10⁴)(5 x 10⁴)

= (5 x 5)(10⁴ x 10⁴)

= 25 x 10^{4 + 4}

= 25 x 10⁸

= 2.5 x 10¹ x 10⁸

= 2.5 x 10^{1 + 8}

= 2.5 x 10⁹

14. Answer :

= (2.5 x 10³) + (9.8 x 10³)

Factor 10³.

= (2.5 + 9.8) x 10³

= 12.3 x 10³

= 1.23 x 10¹ x 10³

= 1.23 x 10^{1 + 3}

= 1.23 x 10⁴

15. Answer :

= (2.78 x 10²) + (5.63 x 10⁵)

= (0.00278 x 10³ x 10²) + (5.63 x 10⁵)

= (0.00278 x 10^{3 + 2}) + (5.63 x 10⁵)

= (0.00278 x 10⁵) + (5.63 x 10⁵)

Factor 10³.

= (0.00278 + 5.63) x 10⁵

= 5.63278 x 10⁵

16. Answer :

= (7.58 x 10²) + (6.45 x 10^-1)

= (7.58 x 10²) + (0.00645 x 10³ x 10^-1)

= (7.58 x 10²) + (0.00645 x 10^{3 + (-1)})

= (7.58 x 10²) + (0.00645 x 10^{3 - 1})

= (7.58 x 10²) + (0.00645 x 10²)

Factor 10².

= (7.58 + 0.00645) x 10²

= 7.58645 x 10²

17. Answer :

= (5.64 x 10³) - (3.98. x 10³)

Factor 10³.

= (5.64 - 3.98) x 10³

= 1.66 x 10³

18. Answer :

= (3.99 x 10²) - (4.7. x 10^-2)

= (3.99 x 10²) - (0.00047 x 10⁴ x 10^-2)

= (3.99 x 10²) - (0.00047 x 10^{4 + (-2)})

= (3.99 x 10²) - (0.00047 x 10^{4 - 2})

= (3.99 x 10²) - (0.00047 x 10²)

Factor 10².

= (3.99 - 0.00047) x 10²

= 3.98953 x 10²

19. Answer :

Three hundred thousand = 300000

In 300000, there is no decimal point. So, assume there is a decimal point at the end.

300000.

Add the decimal point after the first nonzero digit.

3.00000

The decimal point is shifted five digits to the left. Take 5 as exponent for 10 and 10⁵ can be used to write the given number in standard form.

300000 = 3.0 x 10⁵

20. Answer :

Five million = 5000000

In 5000000, there is no decimal point. So, assume there is a decimal point at the end.

5000000.

Add the decimal point after the first nonzero digit.

5.000000

The decimal point is shifted six digits to the left. Take 6 as exponent for 10 and 10⁶ can be used to write the given number in standard form.

5000000 = 5.0 x 10⁶

21. Answer :

= 5000000 x 3000

= (5.0 x 10⁶) x (3.0 x 10³)

= (5.0 x 3.0) x (10⁶ x 10³)

= 15 x 10^{6 + 3}

= 15 x 10⁹

= 1.5 x 10¹ x 10⁹

= 1.5 x 10^{1 + 9}

= 1.5 x 10¹⁰

22. Answer :

= 2500 kilograms

= 2500 x 1000 grams

= 2500000 grams

= 2.5 x 10⁶ grams

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